中文摘要：

基于中心极限定理的合成孔径雷达（SAR）图像统计分布不能反映高分辨率SAR图像尖峰和厚尾的统计特征. 文中使用广义中心极限定理，由雷达回波的实部和虚部的对称稳定分布，得到SAR图像的拖尾分布（幅值图像的拖尾Rayleigh分布以及强度图像的拖尾指数分布），并以拖尾Rayleigh分布为例，讨论了拖尾分布的代数拖尾特征以及尖峰厚尾的统计特性. 为了实现拖尾分布对高分辨率SAR图像的精确建模，基于第二类统计量，提出了对数累积量的参数估计方法，从而高效估计出拖尾分布的参数. 真实SAR图像的建模实例表明，基于广义中心极限定理的拖尾分布可以精确描述高分辨率SAR图像的尖峰和厚尾的统计特征.孙增国’’’韩崇昭。’

英文摘要：

Statistical distributions of synthetic aperture radar （SAR） images based on central limit theorem cannot reflect the statistical characteristics of sharp peak and heavy tail of high-resolution SAR images. By using the generalized central limit theorem, the heavy-tailed distributions （heavy-tailed Rayleigh distribution for amplitude image and heavy-tailed exponential distribution for intensity image） are obtained from the symmetric stable distributions of real and imaginary parts of echoes. Taking the heavy-tailed Rayleigh distribution as an example, the algebraic tails of heavy-tailed distributions are explained as well as the statistical properties of sharp peak and heavy tail. In order to model the high-resolution SAR images with the heavy-tailed distributions, based on second-kind statistical, Characteristics the log-cumulant estimator is proposed to efficiently estimate the parameters of the heavy-tailed distributions. Modeling experiments on real SAR images demonstrate that the heavy-tailed distributions based on the generalized central limit theorem can accurately describe the sharp-peaked and heavy-tailed statistical characteristics of high-resolution SAR images.